Combined Lattice Boltzmann and phase-field simulations for incompressible fluid flow in porous media

A Lattice-Boltzmann method for incompressible fluid flow is coupled with the dynamic equations of a phase-field model for multiple order parameters. The combined model approach is applied to computationally evaluate the permeability in porous media. At the boundaries between the solid and fluid phases of the porous microstructure, we employ a smooth formulation of a bounce-back condition related to the diffuse profile of the interfaces. We present simulations of fluid flow in both, static porous media with stationary non-moving interfaces and microstructures performing a dynamic evolution of the phase and grain boundaries. For the latter case, we demonstrate applications to dissolving grain structures with partial melt inclusions and computationally analyse the temporal evolution of the microporosity under wetting conditions at the melt-grain boundaries. In any development state of the material, the Darcy number and the hydraulic conductivity of the porous medium are evaluated for various types of fluid.

[1]  Gustav Amberg,et al.  Phase-field simulation of dendritic growth in a shear flow , 1998 .

[2]  Rongzheng Wan,et al.  Lattice Boltzmann model with nearly constant density. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  R. Benzi,et al.  Lattice Gas Dynamics with Enhanced Collisions , 1989 .

[4]  D. d'Humières,et al.  Multiple–relaxation–time lattice Boltzmann models in three dimensions , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[5]  Qisu Zou,et al.  A improved incompressible lattice Boltzmann model for time-independent flows , 1995 .

[6]  A. Karma,et al.  Regular Article: Modeling Melt Convection in Phase-Field Simulations of Solidification , 1999 .

[7]  Dongxiao Zhang,et al.  Unified lattice Boltzmann method for flow in multiscale porous media. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  O. Filippova,et al.  Grid Refinement for Lattice-BGK Models , 1998 .

[9]  B. Nestler,et al.  A Lattice‐Boltzmann model to simulate the growth of dendritic and eutectic microstructures under the influence of fluid flow , 2009 .

[10]  L. Luo,et al.  Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation , 1997 .

[11]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[12]  Dierk Raabe,et al.  Overview of the lattice Boltzmann method for nano- and microscale fluid dynamics in materials science and engineering , 2004 .

[13]  Britta Nestler,et al.  A multi-phase-field model of eutectic and peritectic alloys: numerical simulation of growth structures , 2000 .

[14]  W. Miller,et al.  CRYSTAL GROWTH KINETICS AND FLUID FLOW , 2003 .

[15]  Gábor Házi,et al.  Simulation of two-dimensional decaying turbulence using the >incompressible> extensions of the lattice Boltzmann method , 2006 .

[16]  B. Stinner,et al.  Multicomponent alloy solidification: phase-field modeling and simulations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  J. Jiménez,et al.  Boltzmann Approach to Lattice Gas Simulations , 1989 .

[18]  L. Luo,et al.  Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation , 1997 .

[19]  S. Boccaletti,et al.  The control of chaos: theory and applications , 2000 .

[20]  Donald M. Anderson,et al.  A phase-field model with convection: sharp-interface asymptotics , 2001 .

[21]  Dmitry Medvedev,et al.  Lattice Boltzmann scheme for crystal growth in external flows. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Suman Chakraborty,et al.  An enthalpy-based lattice Boltzmann model for diffusion dominated solid–liquid phase transformation , 2005 .

[23]  Suman Chakraborty,et al.  A hybrid lattice Boltzmann model for solid–liquid phase transition in presence of fluid flow , 2006 .

[24]  A. Karma,et al.  Phase-field simulations of dendritic crystal growth in a forced flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  D. Kehrwald.  Parallel lattice Boltzmann simulation of complex flows , 2004 .

[26]  P. Lallemand,et al.  Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[28]  S. Succi,et al.  A Lattice Boltzmann Model for Anisotropic Crystal Growth from Melt , 2002 .

[29]  Bernie D. Shizgal,et al.  Rarefied Gas Dynamics: Theory and Simulations , 1994 .

[30]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[31]  Jacob Bear,et al.  Transport Phenomena in Porous Media , 1998 .

[32]  S Succi,et al.  Lattice Boltzmann model for anisotropic liquid-solid phase transition. , 2001, Physical review letters.

[33]  Harald Garcke,et al.  Phase-field model for multiphase systems with preserved volume fractions. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  S. Succi,et al.  Mesoscopic Models of Liquid/Solid Phase Transitions , 1998 .

[35]  K. Kassner,et al.  Lattice-Boltzmann scheme for dendritic growth in presence of convection , 2005 .